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SUMMARY:H-minimality (with R. Cluckers\, I. Halupczok)
DTSTART:20220419T131500
DTEND:20220419T150000
DTSTAMP:20260506T004944Z
UID:0f44a2dc763510bd40d1a9c7b6dccd50fd6e551c551796f67d1e4629
CATEGORIES:Conferences - Seminars
DESCRIPTION:Silvain Rideau-Kikuchi (Université de Paris)\nThe development
  and numerous applications of strong minimality and later o-minimality has
  given serious credit to the general model theoretic idea that imposing st
 rong restrictions on the complexity of arity one sets in a structure can l
 ead to a rich tame geometry in all dimensions. O-minimality (in an ordered
  field)\, for example\, requires that subsets of the affine are finite uni
 ons of points and intervals.\n\nIn this talk\, I will present a new minima
 lity notion (h-minimality)\, geared towards henselian valued fields of cha
 racteristic zero\, generalising previously considered notions of minimalit
 y for valued fields (C\,V\,P …) that does not\, contrary to previously d
 efined notions\, restrict the possible residue fields and value groups. By
  analogy with o-minimality\, this notion requires that definable sets of o
 f the affine line are controlled by a finite number of points. Contrary to
  o-minimality though\, one has to take special care of how this finite set
  is defined\, leading us to a whole family of notions of h-minimality. I w
 ill then describe consequences of h-minimality\, among which the jacobian 
 property that plays a central role in the development of motivic integrati
 on\, but also various higher degree and arity analogs.
LOCATION:GC A1 416 https://plan.epfl.ch/?room==GC%20A1%20416
STATUS:CONFIRMED
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